Complex scale feature extraction for gearbox via adaptive multi-mode manifold learning

The transient impacts with sideband modulation caused by some fault of gearbox are the technical basis for fault diagnosis, which will be inevitably interfered by heavy background noise distributed in complex modulation frequency bands. Generally, only the principle components under the selected scale is remained and analyzed as the evidence of fault diagnosis, while some crucial features spread in other scales are ignored. Specially, the selected signal still has lots of in-band noise interference. Motivated by these issues, a new adaptive multi-mode manifold learning (AM(2)ML) method is proposed to enhance the useful gearbox features distributed complex scales with the in-band noise suppressed. Firstly, a series of mode components are obtained by adaptive variational mode decomposition, where the optimal decomposition level is automatically achieved by the k-value. Time-frequency manifold learning is then respectively employed to mine their corresponding potential structural characteristics. And a reconstructed signal contained multi-scale features are represented via the proportion weights of the correlation coefficients. Therefore, the denoised signal of each manifold mode will be rebuilt by phase preserving and a series of inverse transform while the in-band noise is suppressed. With the weight coefficients of each mode, the final multi-scale features are synthesized. As the result shows, the sub-band energy ratio is introduced to evaluate the effectiveness of the method. The sub-band energy ratio of AM(2)ML method is about 3 times of VMD method, and about 2 times of fast-kurtogram method. It can be seen that the multiple modes can be adaptively decomposed with the complex scale structural characteristics enhanced by manifold learning, and the expected characteristics distributed in all scales can be well rebuilt via a dynamic weight reconstruction in a self-learning way. The effectiveness of the proposed AM(2)ML method is verified by the self-made gearbox.